Lévy laws and 1/f noises are shown to emerge uniquely and universally from a general model of systems which superimpose the transmissions of many independent stochastic signals. The signals are considered to follow, statistically, a common - yet arbitrary - generic signal pattern which may be either stationary or dissipative. Each signal is considered to have its own random transmission amplitude and frequency. We characterize the amplitude-frequency randomizations which render the system output's stationary law and power-spectrum universal - i.e., independent of the underlying generic signal pattern. The classes of universal stationary laws and power spectra are shown to coincide, respectively, with the classes of Lévy laws and 1/f noises - thus providing a unified and universal explanation for the ubiquity of these classes of "anomalous statistics" in various fields of science and engineering.
|Number of pages||4|
|Journal||Proceedings of the National Academy of Sciences of the United States of America|
|State||Published - 28 Jul 2009|
- Anomalous statistics
- Poissonian randomizations
- Shot noise